Short of me digging through boxes of old college textbooks and such, I must wave my hands about as I struggle with memory. Here goes: essentially the number o

Short of me digging through boxes of old college textbooks and such, I must wave my hands about as I struggle with memory. Here goes: essentially the number of particle "generations" (with the first generations of leptons being the electron, the positron, the electron neutrino, and the electron anti-neutrino) has an effect on the abundance of the "light elements" like Helium-4 during the early phase of the universe. This was pointed out as a dependence in roughly the 1960s by Hoyle (yes, that Hoyle) and Tayler. Each generation would increase the density of the early universe, causing it to expand faster, and in turn the earlier the transmutations of light elements would have stopped, leaving excess neutrons to go around. This means more Helium-4. So, measure the Helium-4 abundance and you can set some error bars on the number of generations. So the tau particle, in generation three, was predicted around 1971 and finally detected about six years later. Of course the Nobel for this discovery wasn't awarded until much later but everyone was on tenterhooks: could we find a fourth generation? Could it exist? But we didn't have the measurements of the early universe nailed down at the time. Measurements of the abundance of these elements around the late eighties or early nineties is in line with the number of generations being three, but it could be four at the "couple of sigma" level of confidence. Indeed, originally it was thought that four was an upper limit in the 1980s. And so here we are. For a fourth generation, the equivalent of the electron mass would be >> 45 GeV/c². Simply enormous. My guess is that further observations have pushed the confidence of "three" much much higher since then, but I haven't been paying attention. Of course, the generations aren't confined to leptons (the "lightest" particles), but also to the quarks. So the first generation has its mirror in the up quark, the anti-up quark, the down quark, and the anti-down quark. Again, one of those symmetries I brought up.